Without looking at the manual, i would say yes, the control unit requires 12volt DC to run. The TS stator is 12v 3 phase, fed into a regulator rectifier that changes the AC from the stator into DC to charge the battery. The exhaust control unit is then powered from the 12v DC from battery. You could probably get away with no battery and just use a large capacitor. Well thats what i reckon anyway, but i might be wrong because dont the RM's have this valve too and they dont have a battery, so maybe they run by AC?
Anyway do you have a wiring diagram there? I do so i will have a look at it now.